1. Math notebook, pencil and calculator Conditional Relative Frequencies and Association

2. Relative Frequency How often something happens divided by all outcomes. Example: if your team has won 9 games from a total of 12 games played: * the Frequency of winning is 9 * the Relative Frequency of winning is 9/12 = 75%

3. Conditional Relative Frequency A conditional relative frequency compares a frequency count to the marginal total that represents the condition of interest.

4. Example The condition of interest in the first row is females. The row conditional relative frequency of females responding “Invisibility” as the favorite superpower is 48/228 or approximately 0.211. This conditional relative frequency indicates that approximately 21.1% of females prefer “Invisibility” as their favorite superpower. Similarly, 27/222, or approximately 0.122 or 12.2%, of males prefer “Invisibility” as their favorite superpower. FlyFreeze TimeInvisibilityStrengthTelepathyTotal Females496048170228 Males5171272548222 Total1001317526118450

5. Questions How is relative frequency calculated? How could we determine a relative frequency for only the female students?

6. What is? The conditional relative frequency of females who choose “to fly” as a superpower: 49/ 228 ≈ 0.215 21.5%.

7. Use the frequency counts from the table to calculate the missing row conditional relative frequencies. Round the answers to the nearest thousandth.

8. Questions Suppose that a student is selected at random from those who completed the survey. What do you think is the gender of the student selected? What would you predict for this student’s response to the superpower question? Suppose that a student is selected at random from those who completed the survey. If the selected student is male, what do you think was his response to the selection of a favorite superpower? Explain your answer.

9. Two categorical variables are associated if the row conditional relative frequencies (or column relative frequencies) are different for the rows (or columns) of the table. For example, if the selection of superpower selected for females is different than the selection of superpowers for males, then gender and superpower favorites are associated. This difference indicates that knowing the gender of a person in the sample indicates something about their superpower preference.

10. If you knew that a person was female, could you predict that she spends more than 30 minutes getting ready for school? If you knew that a person was male, could you predict that country music is his favorite type of music?

11. For what superpowers would you say that the conditional relative frequencies for females and males are very different? For what superpowers are the conditional relative frequencies nearly equal for males and females? Suppose a student is selected at random from the students who completed the survey. If you had to predict which superpower this student selected, would it be helpful to know the student’s gender? Explain your answer.

12. Let’s Look A conditional relative frequency compares a frequency count to the marginal total that represents the condition of interest. The differences in conditional relative frequencies are used to assess whether or not there is an association between two categorical variables. The greater the differences in the conditional relative frequencies, the stronger the evidence that an association exits. An observed association between two variables does not necessarily mean that there is a cause-and-effect relationship between the two variables